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Microseismicity and creeping faults: Hints from modeling the

Hayward fault, California (USA)

R. Malservisia,T,1, K.P. Furlongb, C.R. Gansb

aUniversity of Miami, RSMAS, MGG, 4460 Rickenbacker, Cswy, Miami, FL, 33134, USAbGeodynamics Research Group, Penn State University, Department of Geosciences, 542 Deike Building, University Park, PA, 16802, USA

Received 31 August 2004; received in revised form 1 February 2005; accepted 17 February 2005

Editor: S. King

Abstract

Creeping segments of strike-slip faults are often characterized by high rates of microseismicity on or near the fault. This

microseismicity releases only a small fraction of the slip occurring on the fault and the majority of the accumulating elastic

strain is released either through aseismic creep or in rare large events. Distinguishing between creeping or non-creeping patches

on faults and determining the resulting accumulated slip deficit is important in assessing the seismic hazard associated with a

fault. Unfortunately, surface creep data alone are insufficient to constrain the creep at depth on the fault. Here we analyze the

possibility of using microseismicity as a further constraint. An analysis of the accumulation of Coulomb stress associated with

the fault creep indicates that the transition from creeping regions to locked patches ha s the potential to affect the local seismicity

pattern. Precise relative relocations of the microseismicity of the Hayward fault [1] [F. Waldhauser, W.L. Ellsworth, Fault

structure and mechanics of the Hayward Fault, California, from double-difference earthquake locations, J. Geophys. Res.

107(3), doi:10.1029/2000JB000084 , 2002.] indicate that a fraction of the events repeat, indicating recurrent ruptures of the

same small patch. A comparison of the creeping pattern resulting from a Finite Element deformation Model with this precisely

relocated microseismicity indicates that the non-repeating earthquakes mainly occur in the transitional zones from creeping to

locked patches, while recurrent (repeating) earthquakes cluster in high creep-rate regions. Building from this observation, we

have developed an analysis approach to better define patterns of creep, and thus the slip deficit, on the Hayward fault.

Additionally this creep rate and its spatial pattern on the fault vary as a function of time after the system is loaded by

earthquakes on the locked patches.

D 2005 Elsevier B.V. All rights reserved.

Keywords: microseismicity; creeping faults; Coulomb stress; Hayward fault; seismic hazard

1. Introduction

A characteristic of some faults is the accommoda-

tion of part of the inter-seismic differential motion

0012-821X/$ - see front matterD 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.epsl.2005.02.039

T Corresponding author. Ludwig-Maximilian University, Section

of Geophysics, Theresienstr. 41, Munich D-80333, Germany. Tel.:

+49 89 2180 4201.

E-mail address: [email protected],

[email protected] (R. Malservisi).1 Tel.: +1 305 361 4928.

Earth and Planetary Science Letters 234 (2005) 421435

www.elsevier.com/locate/epsl
http://dx.doi.org/doi:10.1029/2000JB000084http://dx.doi.org/doi:10.1029/2000JB000084http://dx.doi.org/doi:10.1029/2000JB000084http://dx.doi.org/doi:10.1029/2000JB000084


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through fault creep. While most faults and fault

segments remain locked between major seismic

events, creeping fault segments accommodate some

fraction of the motion by slipping essentially aseismi-cally. Creeping faults were first identified along the

San Andreas Faults in central California, where

cultural features were progressively offset [2]. Apart

from the San Andreas fault system in California

(which includes the Hayward fault, Fig. 1) [35]

significant creep at the surface seems to be rare [6] but

it has been suggested for segments of faults in strike-

slip and trans-compressional regimes [710]. On the

other hand, creep seems to be quite common at theplate interface in the seismogenic zone in non-fully-

coupled subduction zones (e.g. [11,12]). Because

most creeping faults appear to release only part of

the long-term motion through aseismic slip, they still

accumulate a slip deficit; accumulated elastic strain

SF

PP

BK

OA

FR

SANANDREASFAU

LT

CALAVERASFAULT

HAYWARDFA

ULT

1868Rupture

-122.6 -122.4 -122.2 -122.0

37.6

37.8

38.0

Oaklandlocked patch

Fig. 1. San Francisco Bay area map with Hayward fault seismicity. The map shows geographical references used in the text and the main faults

of the San Andreas fault system [38]. The relocated seismicity from Waldhauser and Ellsworth [1] is indicated by the small solid dots. Our study

area in the vicinity of the Hayward fault is highlighted by the gray shaded box; the surface trace of the fault is marked by the thicker line. The

double arrow indicates the maximum inferred length of fault rupture during the 1868 earthquake. There is uncertainty about the extent of the

1868 rupture north of Oakland and south of Fremont [24,25]. The insert shows the position of the Bay area with respect to California (PP: Point

Pinole, BK: Berkeley, OA Oakland, FR: Fremont, SF: San Francisco).

R. Malservisi et al. / Earth and Planetary Science Letters 234 (2005) 421435422


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that is periodically released by medium to large

earthquakes. Determining the slip deficit accumulated

by a fault is critical for any seismic hazard assessment

for the surrounding regions. Unfortunately, models offault creep constrained only by surface creep obser-

vations are highly non-unique and not overly sensitive

to the details of the slip behavior at depth, indicating

the need for further constraints [13,14].

In general, faults observed to creep also generate

significant numbers of small earthquakes on or near

the fault [15] and it is common practice to identify

creeping segments as those characterized by this on-

fault microseismicity [1,15,16]. Although this micro-

seismicity occurs at a high rate, because of its low

magnitude range it does not contribute significantly tototal fault slip [15,17,18]. The microseismicity asso-

ciated with creeping faults has been previously

inferred to represent small frictionally-locked patches

that slide in an unstable way, surrounded by larger

regions of stable sliding [1,1921]. Here, we suggest

that this mechanism is responsible only for one part of

the microseismicity and that the strain associated with

the transition from locked to creeping patches on the

fault can generate a large fraction of the micro-seismicity in the surrounding strained crust. Further

we have analyzed the potential for using micro-

seismicity as an aid in constraining the patterns of the

creep on the fault by comparing relocated earthquakes

with stress, strain, and creep, determined using a 3D

Finite Element Model (FEM) that incorporates real-

istic rheologies.

2. Hayward fault

The Hayward fault (Fig. l), east of the San

Francisco Bay, CA (USA) is a classic example of a

creeping fault. Although in some areas the creep at

the surface appears to accommodate more than 50%

of the long-term displacement [22], the combination

effective strain rate (10-14 s-1)

1 2 3 4 5

2 4 6 8

Creep Rate (mm/yr)

0

Locked

12km

82 km

1868

PP BK OA FRa)

b)

0 10 20 30 40 50 60 70Position (km)

4.0 3.0 2.0 1.0Magnitude

CREEP RATE

STRAIN RATE

Fig. 2. Fault creep rate and effective strain rate. (a) Fault c reep rate for the model 7c-HN from Malservisi [39]. The open circles represent the

relocated microseismicity from Waldhauser and Ellsworth [1] (seismicity from 1984 to 1998) projected on the fault plane. As in all following

figures, we project seismicity up to 2 km from the fault plane (gray box in Fig. 1). The dimension of the circle is scaled with the event magnitude

(magnitude from 0.5 to 3.5). PP, BK, OA and FR as in Fig. 1. The arrow labeled 1868 indicates the estimated maximum extent of the 1868

rupture. (b) Effective strain rate in the crust surrounding the fault ( computed 500 m from the fault plane). We use the effective strain rate

(defined asffiffiffiffiffiffiffiffiffiffiffiffi

12eeijee ij

q) as a measure of the magnitude of the strain rate [40]. In this case the effective strain rate is comparable to the shear strain.

R. Malservisi et al. / Earth and Planetary Science Letters 234 (2005) 421435 423


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of creep plus microseismicity does not account for

the long-term slip and the fault does experience

moderate to large earthquakes [23,24]. Currently the

Hayward fault is listed by the Working Group forCalifornia Earthquake Probability (WGCEP) as the

highest hazard in the Bay region, although that

estimation is also associated with the lowest reli-

ability [22]. The most recent significant event on the

Hayward fault is associated with the rupture of the

southern segment in 1868 in a magnitude ~6.8

earthquake [23,24]. There is evidence that the last

earthquake on the norther n s egment occurred

between 1640 and 1776 AD [2326].

The pattern of observed surface creep along the

Hayward fault[5,27] implies a complexity of creep onthe fault plane. Several studies have investigated

possible patterns of fault creep on the Hayward fault

compatible with surface creep observations [13,17,28

30]. In focusing on the response of a creeping fault to

different geometries of locked patches and the

interaction of the fault with the surrounding litho-

sphere, Malservisi et al. [13] showed that creep on the

fault plane increases smoothly from locked patches to

fully creeping areas (Fig. 2). This transition produces a

gradient in creep on the fault plane and thus generates

strain in the crust immediately adjacent to the fault. We

infer that this strain may be sufficient to generate the

diffuse microseismicity on and adjacent to the creeping

fault. With this framework, microseismicity can be

used to map patterns of creep on faults. The

combination of high quality surface creep data

[27,29], studies modeling creep and slip deficit

[13,14,2830], and precisely relatively relocated

microseismicity [1] allows us to develop a new

approach to map patterns of on-fault creep.

3. Hayward fault and microseismicity

Waldhauser and Ellsworth [1] provide precisely

relatively relocated events for the Hayward fault.

Their seismicity data spans 19841998 with magni-

tudes ranging from 0.5 to 3.5. In spite of the high

frequency of events, the total slip produced by the

microseismicity is negligible compared to slip occur-

ring through creep [17]. Here we combine the recent

study by Waldhauser and Ellsworth [1] of precisely

relocated seismicity along the Hayward fault with our

3D model of creep (Model 7c-HN, [13]) to test the

hypothesis that deformation in the locked-to-free

transition zone generates the observed microseismic-

ity. A comparison of the relocated seismicity with thepatterns of creep on the fault and the resulting strain

rate in the adjacent crust (Fig. 2) indicates a clustering

of events in the transitional areas where the surround-

ing crust has high strain rate. As indicated above,

despite the low friction assigned to those parts of the

fault, the regions bshadowedQ by the surrounding

locked patches have a low creep rate, thus accumulate

slip deficit while the surrounding crust is strained. In

model 7c-HN, for example, the maximum strain rate

occurs in the region surrounding the locked area

beneath Oakland (darkest gray in Fig. 2b) and alongthe border of the creeping section of the fault. Plotting

the relocated microseismicity over the strain/creep rate

maps (Fig. 2) indicates that it clusters in these high

strain rate (N21014 s1) or equivalently slow

creep rate (b22 mm/yr) regions.

We have quantified this correlation between seis-

micity and creep rates by categorizing the seismicity

into creep and/or strain rate bins, computing how much

seismicity occurs for each category of creep. As we did

in a previous publication [17], the moment associated

with each tabulated magnitude was computed using a

relation developed by Thatcher and Hanks [31] for

Southern California (to convert magnitude to energy)

and the relationship from Abercombie [32] (to trans-

late energy to moment). Due to the related uncertainty

in correlating the reported magnitude with either

seismic moment or energy for the relatively small

earthquakes of our study (magnitudes ranging from 0.5

to 3.5), the results are presented both as sum of

moment (Table 1) and as sum of magnitude (Table 2).

If we exclude the two magnitude 3.5 earthquakes south

of the locked region, the conclusions from the two

methods are consistent. In the following analysis wediscuss only the moment case.

Table 1 summarizes the percentage of cumulative

moment released by the earthquakes in the different

creep/strain categories with the exclusion of two

magnitude 3.5 events. The two bigger events of our

catalog were excluded because their moment repre-

sents more than 40% of the total moment released by

the earthquake in the catalog and would bias the

statistics. When compared to model 7c-HN, 54% of

the total moment of the relocated earthquakes is



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released in the region creeping less than 2 mm/yr(strain rate N1.51014 s1), a region that corre-

sponds to only 31% of the fault area. In contrast, 28%

of the seismicity is released in the fully creeping

region (rate N4 mm/yr) which corresponds to ~29%

of the area. A close analysis of Fig. 2 also shows that

many of the events assigned to the locked patches are

located close to the edge of those patches. Incidentally

we want to note that the two relatively bigger

earthquakes happen in this transitional area as well;

if we include those events, 93% of the moment is

released in regions creeping less than 2 mm/yr. This

observation is in agreement with the results of Tse et

al. [33], who found that stress concentrates at the

border of locked patches.

In their study, Waldhauser and Ellsworth [1]

identified a subset of earthquakes that appear to be

repeated ruptures of the same small asperities (solid

circles in Fig. 3a). They referred to this subset as

repeating or recurring earthquakes. It has been argued

that such repeating earthquakes represent very smalllocked patches surrounded by free-slipping regions of

the fault [1921]. Taking into account the rupture size

[17], the resolution in the relocations of the event, the

fact that some of the repeated events are not exactly

co-located (e.g. Fig. 10 of Waldhauser and Ellsworth

[1]), and the incompleteness of the catalog of

recurrent events, we consider here as recurrent all

the events falling within 150 m of events identified as

repeating by Waldhauser and Ellsworth [1]. More than

80% of the summed moment released by repeated

earthquakes is in the fully-creeping area, consistent

with the model of these events representing small

locked patches (mini-asperities) within a free-slip

region. When we remove the repeating earthquakes

from the data set and repeat the analysis of comparing

cumulative moment with creep rate, we find that

earthquakes in the fully-creeping region (creep rate N4

mm/yr, 29% of area) release only 12% of the total

moment while earthquakes in the high-strain region

Table 2

Percentage of area and of total magnitude assigned to different creep-rate categories

Creep rate 7c-HN (Malservisi et al. [13]) KT3 (this paper)

% Area %P

Magnitude

(all)

%P

Magnitude

(repeating)

%P

Magnitude

(non-repeating)

% Area %P

Magnitude

(all)

%P

Magnitude

(repeating)

%P

Magnitude

(non-repeating)

Locked 10 17.4 10.6 18.8 11 18.5 11.4 19.3

02 mm/yr 21 26.3 17.8 28.1 25 29.7 18.8 30.9

24 mm/yr 40 37.8 5.3 44.3 41 38.2 18.9 46.1

46 mm/yr 29 18.5 66.3 8.8 23 17.8 50.9 3.6

%P

Moment (all): percentage of cumulative magnitude released by all the relocated events.

%P

Moment (repeating): percentage of cumulative magnitude released by the events within in a radius of 150 m from the events defined as

repeating by Waldhauser and Ellsworth [1].

%P

Moment (non-repeating): percentage of the cumulative magnitude released by the relocated events not identified as repeating and not

within 150 m of repeating earthquakes.

Table 1

Percentage of area and of total moment assigned to different creep-rate categories

Creep rate 7c-HN (Malservisi et al. [13]) KT3 (this paper)

% Area %P

Moment(all)

%P

Moment(repeating)

%P

Moment(non-repeating)

% Area %P

Moment(all)

%P

Moment(repeating)

%P

Moment(non-repeating)

Locked 101 29.5 9.1 34.5 11 31.9 9.7 39.3

02 mm/yr 21 24.6 1.7 30.8 25 12.2 0.7 13.7

24 mm/yr 40 17.6 3.3 22.4 41 38.2 2.0 39.2

46 mm/yr 29 28.3 85.9 12.3 23 17.8 87.6 7.8

%P

Moment (all): percentage of cumulative magnitude released by all the relocated events.

%P

Moment (repeating): percentage of cumulative magnitude released by the events within a radius of 150 m from the events defined as

repeating by Waldhauser and Ellsworth [1].

%P

Moment (non-repeating): percentage of the cumulative magnitude released by the relocated events not identified as repeating and not

within 150 m of repeating earthquakes.



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(creep rate b2 mm/yr; 31% of area) release ~65%

(Table 1, Fig. 3).

4. Locked patches and Coulomb stress

A locked patch represents a region on the fault

plane allowing no differential motion across the fault,

except during an earthquake. However, because the

crust surrounding the fault is a continuum, there

cannot be step discontinuities in displacement (except

across the fault itself). As a result, there is a

transitional region from the fully-locked to the free-

slip region of the fault. Although the fault properties

in the transitional area allow free slip, the proximity to

the locked patch reduces the slip on the fault. These

locked and transitional regions slide at a velocity

slower than the surrounding creeping regions and thus

accumulate strain energy within the crust adjacent to

the fault at a faster rate.To test the potential influence of the interaction

between creeping and locked patches on the local

stress field, and thus on the microseismicity, we

analyze the Coulomb stress associated with the

modeled pattern of creep. For this analysis we use

a simplified approach, using Coulomb 2.5 [34] to

determine the rate of Coulomb stress developed. This

simple 3D elastic modeling allows us to focus on the

role of locked and free patches within the elastic

upper crust in generating a distribution of Coulomb

effective strain rate (10-14 s-1)1 2 3 4 5

2 4 6 8Creep Rate (mm/yr)0

Locked

12km

82 km

1868

PP BK OA FR

0 10 20 30 40 50 60 70Position (km)

80

0 10 20 30 40 50 60 70Position (km)

80

a)

b)

c)

Model 7c-HN

Model 7c-HN

Fig. 3. Comparison between non-recurrent earthquakes and model 7c-HN results. (a) Relocated microseismicity along the Hayward fault (open

circles) adapted from [1]. The circles are scaled according to their magnitude (see Fig. 2). The solid circles represent clusters of earthquakes

defined as recurrent by Waldhauser and Ellsworth [1]. In the analysis, we also considered as recurring all the earthquakes within 150 m of these

events. (b) Comparison of fault creep as evaluated in Fig. 2 and non-recurrent seismicity. (c) Comparison between off-fault strain rate from the

model 7c-HN and the non-recurrent microseismicity.



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stress (and seismicity). Similar results are obtained

using more complete 3D viscoelastic modeling. With

such modeling, however, it is difficult to isolate the

effects of the fault patterns from the overall effects ofviscous localization and relaxation in the lower crust.

Using the code Coulomb 2.5, we calculate the yearly

stress changes in an elastic half-space due to creep

on the Hayward fault, derived by model results of

Malservisi et al. [13], assuming steady-state creep.

The absolute value of the Coulomb stress is alsodependent on the regional stress field, an uncertain

parameter. For consistency with our FEM boundary

0

10

20

30

40

50

60

70

80

DistanceFromP

P(km)

-40 -20 0 20 40Distance From HF (km)

.05.04.03.02.01

Optimal Fault Coulomb Stress (bars/yr)

.0-.01-.02-.03-.04-.05

-20

-10

0

-40 -30 -20 -10 0 10 20 30 40

-20

-10

0

-40 -30 -20 -10 0 10 20 30 40

a)

b)

c)

Depth(km)

Depth(km)

Distance From Hayward fault (km)

A

A

A'

A'

B

B B'

B'

Depth 7.5 km

Fig. 4. Results from Coulomb stress computation compared with relocated seismicity. (a) Vertical cross section in a rapidly creeping region

(position ~60 km). Note that the Coulomb stress is low, the seismicity is localized on the fault, and the majority of the seismicity is represented

by repeating events (magenta dots). (b) Vertical cross section in the region beneath Oakland (locked patch). Note the high Coulomb stress,

seismicity diffuse over a large area (~corresponding to the area of high Coulomb stress) and prevalence of non-repeating events (black dots). (c)

Horizontal slice at 7.5 km depth (through the middle of the locked patch beneath Oakland). Boxes represent the areas where the seismicity has

been projected for the vertical cross sections (a and b).



8/15

conditions we assume that regional stress is given by

a simple shear stress parallel to the fault of 6 kPa/yr,

a stress compatible with previous calculations

[35,36].Fig. 4 shows the results from the Coulomb stress

calculation for the best-oriented strike-slip fault

compared with the relocated microseismicity. The

top two panels correspond to two vertical slices

located in the rapidly creeping region in the south

(a) and in the locked region of Oakland (b). The

lowest panel shows a horizontal slice at 7.5 km depth

(at this depth the patch beneath Oakland is locked).

There are several important features of the stress field:

(1) there is negative Coulomb stress correspondingto the rapidly creeping regions. This is compat-

ible with the fact that creep is releasing part of

the elastic strain accumulating at the plate

boundary. The negative Coulomb stress should

map a reduction in the microseismicity in the

surrounding lithosphere. It is interesting to notethat in the low (negative) Coulomb stress region

the microseismicity is mostly aligned with the

fault and the repeated earthquakes (magenta

dots) represent the majority of the activity.

(2) In the transition zone and in the area surround-

ing the locked patch, the Coulomb stress is

positive. In particular we can see that the high

(positive) Coulomb stress region (the region

where the stress regime is more favorable for

the seismicity) is a broad region adjacent to the

fault plane. It is interesting to note that therelocated microseismicity in this area is not

aligned with the fault plane but rather tends to

-40 -30 -20 -10 0 10 20 30 40

Friction 0.4

Distance from the Hayward fault (km)

80

70

60

50

40

30

20

10

0

DistanceFromP

P(km)

A

B

C C

D

D

N

P1

E1

E2B1

B2

S1

S2

S3

H1

H2

F1

F2

F3

B3

Fig. 5. Focal mechanisms for the optimally-oriented fault computed using Coulomb 2.5 [34], a friction coefficient of 0.4, and regional shear

stress from numerical models [13,35,36]. We plot only the right-lateral mechanisms; similar rotations are present for left-lateral ones. Only the

mechanisms in regions of positive Coulomb stress (for strike-slip fault) have been plotted. We enlarge example mechanisms representing

important features (see text for analysis). (A) Regional stress optimally-oriented rupture. (B) Focal mechanisms on the fault plane inside the

locked patch. (C) Mechanisms on the crust surrounding the locked patch. (D) Mechanisms atthe top of the locked patch. The black mechanisms

correspond to the composite focal mechanisms observed by Waldhauser and Ellsworth [1] rotated in the fault parallel reference frame of the

figure. The labels correspond to their naming scheme. Coulomb stress plotted using the same color scale of Fig. 4.



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cluster in a broader region roughly the size of

the positive Coulomb stress area.

(3) The change in Coulomb stress in the transition

from locked to fully-creepable regions alsoshould rotate focal mechanisms. Fig. 5 shows

model-determined focal mechanisms at 7 km

depth oriented in the direction of the maximum

Coulomb stress (the most favorable direction of

slip during a seismic event). For simplicity we

have plotted focal mechanisms only in the

region corresponding to positive Coulomb

stress. The focal mechanisms are highly sensi-

tive to the regional stress and the friction angle;

nevertheless we note a consistent pattern in all

our models. Mechanisms located on the faultplane but within the locked patch (B in Fig. 5)

are similar to mechanisms that would be

produced by the regional stress field. In the

crust to the side of the locked patch (C) the

mechanisms show a change in dip of the rupture

plane. The highest rotation is observed at the tip

of the locked patch (D). Note that although

these results cannot be considered conclusive

due to their sensitivity to the regional stress

field, almost all the composite focal mecha-

nisms from Waldhauser and Ellsworth [1] (with

the exception of S3) have a similar rotation to

the ones computed.

5. Using seismicity to map the fault creep

As discussed above, the transition from a large

locked patch to a fully creepable fault alters the stress

field and thus can influence the amount, distribution,

and the type of seismicity. In particular, we can place

additional constraints on patterns of locked patches and

fault creep by using the observation that the bnormalQ

microseismicity clusters in the transition areas whilethe repeated seismicity is more prevalent in highly

creeping regions. For example, we can add small

locked patches in areas where non-repeated earth-

quakes cluster. The region around position 60 km (Fig.

3) is a good candidate to test this hypothesis. Although

model 7c-HN indicates that this region is fully

creeping, the area produces a significant amount of

non-repeating earthquakes, suggesting the presence of

a locked patch. As shown by Malservisi et al. [13], the

effective strain rate (10-14 s-1)1 2 3 4 5

2 4 6 8

Creep Rate (mm/yr)0

Locked

12km

82 km

1868

PP BK OA FR

0 10 20 30 40 50 60 70Position (km)

80

Fig. 6. Fault creep and strain rate for the model with two locked patches (KT3). The locked patch in the southern segment has been added in

order to reduce the percentage of non-recurrent seismicity in the fully-creeping region.



10/15

surface creep is not highly sensitive to the presence of

deep and/or small locked patches. The addition of the

patch in position 60 km (Fig. 6) modifies the surface

creep rate within the observed errors (Fig. 7). The newclassification of the seismic moment released accord-

ing to creep rate category is reported in Tables 1 and 2.

The addition of the locked patch decreases the

percentage of moment released by the non-repeated

earthquakes in the fully creeping region from 12% to

7%. At the same time, the addition of the locked patch

changes the surface creep pattern only within the

observed errors (Fig. 7). Fig. 6 show that, as expected,

the distribution of the non-repeated earthquakes of

model KT3 closely follows the strain rate pattern of the

crust surrounding the fault plane.With repeated iterations of this process we can

potentially further improve the correlation between

type of seismicity and creep rate. We could for

example add a locked patch near the deep events at

position 20 km and the Berkeley region, or we could

reduce the spatial extent and/or modify the shape of

locked patches (e.g. the cluster of non-repeating

earthquakes suggests that the locked patch beneath

Oakland is not really a simple box shape but may

extend at depth further north). Unfortunately, the

current resolution of our model (the effect of lockedpatches smaller than ~ 5 km2 cannot be analyzed) does

not allow a further refinement. Since this is a first

attempt to use the microseismicity to help constrain

locked/creeping patches on the fault, we have not

extended the application to such fine spatial resolution.

6. Discussion

Observations of surface creep rate are not sufficient

to unequivocally determine the pattern of creep on thefault, particularly at depth. Precise locations for the

microseismicity along creeping faults are potential

tools to better constrain the pattern of locked and

creeping patches on the faults themselves. Another

approach for improving resolution at depth is to use

the surface strain field in the region surrounding the

fault and not merely on-fault creepmeters. In princi-

ple, the use of off-axis data should be somewhat more

sensitive to the deep behavior of the fault and the use

of such a data set should slightly improve the

calculation of slip at depth. Unfortunately, the areas

most sensitive to the behavior of the Hayward fault at

depth are offshore in the San Francisco Bay area to the

west or in the steep hilly area to the east, both regions

not particularly suitable to geodetic measurements.

The Active Tectonics group at the University of

California Berkeley is currently analyzing the avail-

able data from the San Francisco Bay area GPS

network (BARD network) and InSar data [14,37].

Their results show a fault creep pattern similar to the

one we obtained using the microseismicity (KT3) but

in spite of the additional constraints from off-fault

data the creep behavior at depth is still non-uniquelydetermined.

Recurrent seismicity, where earthquakes appear to

be repeated ruptures of the same small asperities,

predominantly occurs within the fully creeping

regions, while the non-recurrent seismicity clusters

in the transitional creeping zones, regions of high

strain rate. With this assumption/observation, we can

refine the pattern of fault creep, as shown by the

above method used to obtain model KT3 for the

Hayward fault.

SurfaceCreepRate(mm/yr)

Position (km)

0 20 40 60 80

0

2

4

6

SN

Model KT37c-HN [12]

PP

Fig. 7. Comparison between observed geodetic data (adapted from

Lienkaemper et al. [27]) and the results of our models. The shaded

area represents the best-fit for long-term surface creep rate along the

Hayward fault. Both the surface creep rate computed by Malservisi

[39] (model 7c-HN, dashed line) and the modified model that uses

seismicity as a further constraint (KT3 this paper, continuous line)

fit the observed data (shaded area). As with all previous models, we

do not account for the high creep rate at the southern end of the fault

(gray data points), which appear to be a result of interactions with

the surrounding faults. The Hayward fault goes offshore at Point

Pinole (PP in Fig. 1, position 12 km). For this reason, the creep rate

in the northernmost area (012 km) is not constrained.



11/15

It is important to note that the transition from

locked to creeping patches is not limited to strike-slip

faults. It also appears to be a fundamental component

in the behavior of the seismogenic zone in non-fully-coupled subduction regions, where one commonly

speaks of the transition from completely locked to

partially locked (or free slipping) while doing an

evaluation of the plate coupling. Mapping the location

of the locked patches is a critical part of hazard

analysis in subduction zones. Because strain is mainly

accumulating in these areas, they become the sites of

dominant moment release. The study of Norabuena et

al. [11] is an example of such behavior. A comparison

of the map of slip on the fault plane obtained by

inverting geodetic observations in the Costa Ricaregion with the microseismicity recorded by a local

array shows a similar pattern to the one we observed,

with the events clustering in the areas surrounding

strongly-coupled patches.

6.1. Moment accumulated by a creeping fault

In general, if one assumes a steady-state behavior

for a creeping fault, it becomes possible to estimate

the slip deficit accumulated by the fault and thus to

further constrain the hazard. As an example, we can

estimate the slip deficit on the Hayward fault, as

generated by creep rate obtained using model KT3,

assuming that the present motion represents the long-

term fault slip rate and that the computed creep rate

can be extrapolated over time. Fig. 8a shows the

resulting slip deficit averaged over the seismogenic

thickness for the 9 mm/yr long-term (i.e. geologic)

slip rate estimated for the Hayward fault [28,29,33].

Poorly-constrained boundary conditions at the north

end of the model (position 010 km, where the fault is

offshore) and fault complexity at the southern end

(position N70 km, where the Hayward interacts with acomplex network of faults) preclude placing signifi-

cance on the slip deficit predicted by our models in

those regions. On the central part of the fault (position

~ 4060 km), the model produces a vertically-aver-

aged slip-deficit accumulation of ~ 6.5 mm/yr. The

accumulated deficit increases around the locked patch

beneath the Oakland region (N7.5 mm/yr). On the

northern segment (position 1030 km), the model

predicts 5 to 6 mm/yr of slip deficit accumulation.

Integrating over the earthquake cycle it is possible to

estimate the total slip deficit accumulated and thus the

amounts of moment (elastic energy) storage on the

fault. Fig. 8b shows the deficit accumulated in a 350

yr period (a time compatible with the recurrenceinterval on the Hayward fault [23,24] and approx-

imately the time since the 17th century event). On the

southern segment (position ~5060 km), the model

generates a slip-deficit accumulation of ~2.5 m over

the period. Subtracting the assumed slip of ~1.9 m

during the 1868 event [25] the net deficit would be on

the order of ~0.6 m. Since the northern limit of the

1868 rupture is not well constrained, the slip deficit in

the Oakland region is difficult to quantify. The large

locked patch will generate the highest slip deficit (on

the order of 3 m) but it is possible that the 1868 eventreleased a large part of this accumulated moment (in

Fig. 9b we assume that this area was affected by the

1868 event [25]). On the northern segment (position

~1030 km) our model produces a slip deficit of ~2

m. The absence of rupture during the 1868 event

marks this region as having the highest present day

accumulated slip deficit.

6.2. Time dependent creep rate

While the pattern of creep on the fault plays a

primary role in the accumulation of slip deficit, the

additional effects of the earthquake cycle, including

the1868 earthquake and previous earthquakes, also

affects the pattern of the net accumulated seismic

moment on the fault. An additional consideration

when evaluating the pattern of accumulated slip

deficit is the possibility for transient creep behavior

throughout the earthquake cycle. In determining slip

deficit through a comparison of the long-term slip rate

with the present pattern of fault creep, we have

implicitly assumed that the creep rate and the pattern

we have found for the present is constant over time. Itis reasonable, however, that large events such as the

1868 earthquake in the southern segment, or a

possible 17th century event for the northern segment,

could have large transient effects on fault creep.

A simple example of this potential post-earthquake

transient effect on creep rate is given in Fig. 9. The

simulation shows the evolution of the creep over the

fault plane of model 7c-HN after an imposed differ-

ential slip of 1 m (corresponding to a magnitude ~6.1

earthquake) on the locked patch beneath Oakland. The



12/15

fault displacement and the stress released by the

earthquake alter the flow in the viscoelastic layer,

inducing faster flow beneath the fault. This faster flow

increases the load on the creeping sections and thus

the creeping rate on the fault plane. These effects

decay exponentially to the steady-state regime over a

time that depends on the local viscosity and fault

rupture geometry. It is interesting to note in the

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 10 20 30 40 50 60 70 80

0

2

4

6

8

0 32 80

1.9

0.0

Assumed 1868 slip

Position (km)

slipdeficit(mm/yr)

350yrslip

deficitaccumulationafter

the

effectof1868event

accumulated slip deficit

(m)

Position (km)

101868

?

?

?

?SLIP DEFICIT RATE

ACCUMULATED SLIP DEFICIT

PP BK OA FR

a)

b)

Slip deficit accumulated in 350 yr w/o 1868 event

Fig. 8. Hayward fault slip deficit. (a) Vertically-averaged slip deficit rate in the seismogenic layer predicted by model KT3 assuming a 9 mm/yr

long-term slip rate on the Hayward fault. The double-arrowed line indicates the extent of the 1868 rupture [21]. (b) Slip deficit accumulated on

the seismogenic layer during the past 350 yr assuming a constant slip deficit rate as in Fig. 9a (continuous line on the northern side, dashed line

for the area affected by 1868 earthquake). For the 350 yr average we subtract the slip released in the 1868 event (1.9 m, inset) from the slipdeficit accumulated in the southern segment of the fault (position N32 km). The slip deficit in the transition from the northern and the southern

segment is dependent on the poorly-constrained extent and coseismic slip of the 1868 earthquake (question marks). The shaded area

schematically shows average slip deficit inferred from the model results. The northern (position 013 km) and the southern (position 7082 km)

ends of the model are not interpreted because the surface creep data are poorly constrained or influenced by the interaction of the surrounding

faults.



13/15

2 4 6 8Creep Rate (mm/yr)

0

-10

0

-10

0

-10

0

-10

0

-10

0

-10

0

-10

0

EQ

10 12

>14

14

Rupture area (1m differential displacement)

Steady State

3 yrs after earthquake






0

1

2

3

4

5

6

7

8

9

0 50 100

CREEPRATE(mm/yr)

Years after the earthqu

a)

b)

Depth(km)

Fig. 9. Transient creep rate on the fault plane after a seismic event on the locked section beneath Oakland. (a) Creep rate on the fault at diffe

displacement is imposed in the dashed area (steady-state figure). The differential displacement is imposed using the split nodes method [41]. Note

at depth. The two symbols in creep rate panel correspond to the two points where we computed the creep rate plot in b. (b) Simulation of the cr

indicated in a after the 1 m displacement seismic event in the locked area beneath Oakland.


14/15

example shown here that the characteristic recovery

time is faster for shallow than for deep regions of

the fault, indicating the possibility that even when

observations at the surface indicate a return to thesteady-state regime, deep regions of the fault can

still be affected by the transient creep. The use of

steady-state assumption for the slip deficit estima-

t io n w il l l ea d t o a n o ve re st im at io n o f t ot al

accumulated slip deficit. For these reasons, knowing

the extent of the rupture and the amount of slip

during the events is crucial for estimating the

current pattern of stored elastic energy accumulated

on the fault. Unfortunately, neither rupture extent

nor slip are well-constrained for the 1868 event and

virtually unconstrained for the 17th century event.These uncertainties complicate attempts at risk

assessment for the region.

The location of the northern termination of the

1868 rupture and the likely decrease in slip magnitude

near that terminus also affects the earthquake cycle

scenario for the fault. A shorter rupture than the one

used in our analysis or a smaller coseismic slip in the

Oakland area (position ~3050 km) would leave a

large slip-deficit accumulation in that locked patch.

Depending on the different 1868 rupture scenarios,

this deficit would have been released to different

amounts, leaving significantly different risk residuals.

It is interesting to note that the Oakland region

appears to have been involved in both the 1868 event

of the southern segment and the 17th century event of

the northern (?) segment [24]. This locked patch

accumulates slip deficit faster than the surrounding

areas. Furthermore, the transition from this large

locked patch to freely-creeping regions induces a

large strain and stress localization at its boundary. Tse

et al. [33] suggested that these regions of higher stress

are responsible for the nucleation of large ruptures,

thus the Oakland locked patch may play some role inthe rupture initiation or the termination of large events

on the Hayward fault.

Acknowledgements

We thank R. Burgmann, S. Cohen, A. Rubin and

an anonymous reviewer for the thorough reviews and

the comments and suggestions that greatly improved

the paper. We are also grateful to C. Ammon, R.

Engel, D. Fisher, and A. Nyblade for their internal

reviews. RM has been supported by several NASA

grants awarded to T.H. Dixon. CRG was supported

under an NSF Graduate Research Fellowship. Thisresearch has been partially supported by the NEHRP

Grant 04HQGR0040.

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